School of Mathematics and Statistics - Theses
Now showing items 1-10 of 172
Integrated Wishart bridges and their applications
This thesis focuses on the study of Wishart processes, which can be considered as the matrix-valued square-root processes. In mathematical finance, the square-root processes find applications in interest rates modelling ...
Coset construction for the N=2 and osp(1|2) minimal models
The thesis presents the study of the N=2 and osp(1|2) minimal models at admissible levels using the method of coset constructions. These sophisticated minimal models are rich in mathematical structure and come with various ...
Sparse composite likelihood approaches for high dimensional data
The idea of the likelihood function, which plays an important role in the his- tory of statistics, has been widely used in many areas in parametric statistics. Composite likelihood approaches are useful tools to make ...
The coupling time for the Ising heat-bath dynamics & efficient optimization for statistical inference
In this thesis we consider two separate topics of study. The first topic concerns the Ising heat-bath Glaubers dynamics. These dynamics describe a continuous time Markov chain, whose states are assignments of spins to each ...
An explained sum of squares approach to nonparametric regression with measurement error
We introduce a new method in nonparametric regression problems in the presence of measurement error, known as the explained sum of squares. We discuss its theoretical properties and provide evidence of practical application ...
Stochastic spatial-temporal models for rainfall processes
Currently clustered rainfall models have been fitted using Generalized Method of Moments (GMM), because typically they have intractable likelihood func- tions. GMM fitting matches theoretical and observed moments of the ...
Enumerative problems in algebraic geometry motivated from physics
This thesis contains two chapters which reflect the two main viewpoints of modern enumerative geometry. In chapter 1 we develop a theory for stable maps to curves with divisible ramification. For a fixed integer r>0, ...
Comparison theorems for torus-equivariant elliptic cohomology theories
In 1994, Grojnowski gave a construction of an equivariant elliptic cohomology theory associated to an elliptic curve over the complex numbers. Grojnowski’s construction has seen numerous applications in algebraic topology ...
CAT(0) structures on link exteriors: variations on a theme
This thesis adapts the cubical CAT(0) Aitchison complex, A(L), of alternating link exteriors to construct CAT(0) polyhedral metric structures, A′(L), on the exterior of various links from cubes and prisms. The first class ...
Transport equations and boundary conditions for oscillatory rarefied gas flows
A wide range of flow phenomena in everyday life can be modelled accurately using classical continuum theory: the Navier-Stokes equations with associated no-slip conditions. However, oscillatory flows generated by nanoscale ...